Two supplementary angles are in the ratio 5 ratio 4 find the angle

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Two supplementary angles are in the ratio 4 : 5. Find the angles.

Supplementary angles are in the ratio 4 : 5

Let the angles be 4x and 5x

It is given that they are supplementary angles

∴ 4x + 5x = 180°x

⇒ 9x = 180°

⇒ x = 20°

Hence, 4x = 4 (20) = 80°

5( x) = 5(20) = 100°

∴ Angles are 80° and 100°

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Page 2

Two supplementary angles differ by 48°. Find the angles.

Given that two supplementary angles are differ by 48°

Let the angle measured is x°

∴ Its supplementary angle will be (180 - x)°

It is given that

(180 - x) - x = 98°

⇒ 180 - 48° = 2x

⇒ 132 = 2x

⇒ x = `132/2`

⇒ x = 66°

Hence, 180 - x = 114°

Therefore, angles are 66° and 114°

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Two supplementary angles are in ratio 5 : 4. Find the angles

Let the angles be 5x and 4x

According to the problem

5x + 4x = 180°

9x = 180°

x = `(180^circ)/9`

x = 20°

∴ Two angles are

(i) 5x = 5 × 20° = 100°

(ii) 4x = 4 × 20° = 80°

Concept: Related Angles - Supplementary Angles

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